Efficient allocation of channels for wireless communication in different network scenarios has become an extremely important topic of recent research. The main challenge lies in the fact that the channel allocation problem is NP-complete. Because of a maximum allowable time limit imposed in practical situations for allocation of channels, sometimes we may need to be satisfied with a near-optimal solution. In this correspondence, we present a discussion on the various challenges and approaches that have been used by different researchers to solve the problem of channel allocation taking into account different interference issues and efficient utilization of available communication channels for cellular mobile (including multimedia communication) environment and cognitive radio based networks. important classes of wireless networks -cellular mobile networks and cognitive radio networks.Mobile computing, particularly over cellular networks, has emerged as an important topic of research because of the need for computing abilities even when people are on the move. Over the last decade, the number of such cellular network dependent mobile users has been increasing nearly exponentially. With the advances in technology, there has been an increasing demand from the mobile users for providing multimedia services like voice, text, still image, and video over wireless networks. On the other hand, the available bandwidth required for such multimedia data communication for a large number of mobile users is very much limited. Such a limited availability of the radio spectrum, signal distortion, and the interference caused by the environment and other mobile users impose an inherent bound on the capacity of such wireless networks. Therefore, developing methods to utilize the scarce radio spectrum efficiently is more critical than ever before.Based on the application scenario, the common ways to design wireless networks are: (i) infrastructure-based network design such as the cellular structure approach, (ii) infrastructure-less networks such as ad hoc networks, and (iii) hybrid networks which uses a mix of infrastructure with ad hoc network architecture and can typically be found in many sensor network applications. In an infrastructurebased network design-such as the cellular networks, the geographical region under consideration is spatially divided into a number of cells-which can be either overlapping or non-overlapping. A base station is established in each cell, and each mobile station in the cell communicates through this base station via a channel assigned by the base station. Several techniques such as frequency division multiplexing (FDM), time division multiplexing (TDM), or

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